{ "cells": [ { "cell_type": "code", "execution_count": 157, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 157, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import display, Latex\n", "from IPython.core.display import HTML\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read()) " ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python version 3.8.5 (default, Jan 27 2021, 15:41:15) \n", "[GCC 9.3.0]\n" ] } ], "source": [ "import sys #only needed to determine Python version number\n", "print('Python version ' + sys.version)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62 TP 4 - Étude de la convergence" ] }, { "cell_type": "code", "execution_count": 159, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "IPython.notebook.set_autosave_interval(300000)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Autosaving every 300 seconds\n" ] } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "%autosave 300\n", "\n", "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "WyG-bTRQE3f6" }, "source": [ "# Étude de la convergence\n", "\n", "Considérons le problème de Cauchy\n", "\n", ">trouver la fonction $y \\colon I\\subset \\mathbb{R} \\to \\mathbb{R}$ définie sur l'intervalle $I=[0,1]$ telle que\n", "$$\n", "\\begin{cases}\n", "y'(t) = y(t), &\\forall t \\in I=[0,1],\\\\\n", "y(0) = 1\n", "\\end{cases}\n", "$$\n", "dont la solution est $y(t)=e^{t}$. \n", "\n", "On se propose d'estimer l'ordre de convergence d'une méthode numérique.\n", "+ Pour chaque schéma, on calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$. On sauvegarde les valeurs de $h_k$ dans le vecteur `H`. \n", "+ Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on sauvegarde toutes ces erreurs dans le vecteur `err_schema` de sort que `err_schema[k]` contient $e_k=\\max_{i=0,\\dots,N_k}|y(t_i)-u_{i}|$. \n", "+ Pour afficher l'ordre de convergence on utilise une échelle logarithmique, i.e. on représente $\\ln(h)$ sur l'axe des abscisses et $\\ln(\\text{err})$ sur l'axe des ordonnées. \n", " En effet, si $\\text{err}=Ch^p$ alors $\\ln(\\text{err})=\\ln(C)+p\\ln(h)$. \n", " En échelle logarithmique, $p$ représente donc la pente de la ligne droite $\\ln(\\text{err})$.\n", "\n", "Remarque: puisque la fonction $\\varphi(t,y)=y$ est linéaire, toute méthode implicite peut être rendue explicite par un calcul élémentaire en explicitant directement pour chaque schéma l'expression de $u_{n+1}$. Cependant, nous pouvons utiliser le le module `SciPy` sans modifier l'implémentation des schémas (mais on payera l'ordre de convergence de `fsolve`).\n", "\n", "Estimer l'ordre de convergence des méthodes:\n", "1. EE, AB$_2$, AB$_3$, AB$_4$, AB$_5$, N$_2$, N$_3$, N$_4$\n", "2. EI, CN, AM$_1$, AM$_2$, AM$_3$, AM$_4$, BDF$_2$, BDF$_3$\n", "3. EM, Heun, RK4-1, RK4-2\n", "4. AM$_4$-AB$_1$, AM$_4$-AB$_2$, AM$_4$-AB$_3$\n", " \n", "\n", "**Attention: les schémas multistep ont besoin d'initialiser plusieurs pas de la suite définie pas récurrence pour pouvoir démarrer. \n", "Dans cette étude, au lieu d'utiliser un schéma d'ordre inférieur pour initialiser la suite, on utilisera la solution exacte (en effet, l'utilisation d'un schéma d'ordre inférieur dégrade l'ordre de précision).**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On écrit les schémas numériques :\n", "+ les nœuds d'intégration $[t_0,t_1,\\dots,t_{N}]$ sont contenus dans le vecteur `tt` (qui change en fonction de `h`) \n", "+ les valeurs $[u_0,u_1,\\dots,u_{N}]$ pour chaque méthode sont contenues dans le vecteur `uu`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Schémas explicites" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "y69SGZjfIDo9" }, "source": [ "### Schéma de Adam-Bashforth à 1 pas = schéma d'Euler progressif\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi(t_n,u_n)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "_Bgo6mNyIQgu" }, "outputs": [], "source": [ "def EE(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " uu.append(uu[i]+h*phi(tt[i],uu[i]))\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "bJ2pbhejIQM2" }, "source": [ "### Schéma de Adam-Bashforth à 2 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(3\\varphi(t_n,u_n)-\\varphi(t_{n-1},u_{n-1})\\Bigr)& n=1,2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "g38fKrIgSiBQ" }, "outputs": [], "source": [ "def AB2(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " uu.append( uu[i] + (3*k1-k2)*h/2 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "nI8swyc6RxIR" }, "source": [ "### Schéma de Adam-Bashforth à 3 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=u_n+\\frac{h}{12}\\Bigl(23\\varphi(t_n,u_n)-16\\varphi(t_{n-1},u_{n-1})+5\\varphi(t_{n-2},u_{n-2})\\Bigr)& n=2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 162, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "3ymFHJHrSkOh" }, "outputs": [], "source": [ "def AB3(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " for i in range(2,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " uu.append( uu[i] + (23*k1-16*k2+5*k3)*h/12 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "awcWzBp7SXvQ" }, "source": [ "### Schéma de Adam-Bashforth à 4 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{n+1}=u_n+\\frac{h}{24}\\Bigl(55\\varphi(t_n,u_n)-59\\varphi(t_{n-1},u_{n-1})+37\\varphi(t_{n-2},u_{n-2})-9\\varphi(t_{n-3},u_{n-3})\\Bigr)& n=3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 163, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "-r1BaNeLTrHq" }, "outputs": [], "source": [ "def AB4(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " uu.append( uu[i] + (55*k1-59*k2+37*k3-9*k4)*h/24 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "heLmvMe_S0y6" }, "source": [ "### Schéma de Adam-Bashforth à 5 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{4}=y_4,\\\\\n", "u_{n+1}=u_n+\\frac{h}{720}\\Bigl(1901\\varphi(t_n,u_n)-2774\\varphi(t_{n-1},u_{n-1})+2616\\varphi(t_{n-2},u_{n-2})-1274\\varphi(t_{n-3},u_{n-3})+251\\varphi(t_{n-4},u_{n-4})\\Bigr)& n=4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 164, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "yPXMx8CITt4C" }, "outputs": [], "source": [ "def AB5(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " uu.append(sol_exacte(tt[4]))\n", " for i in range(4,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " k5 = phi( tt[i-4], uu[i-4] )\n", " uu.append( uu[i] + (1901*k1-2774*k2+2616*k3-1274*k4+251*k5)*h/720 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "OldEmxFfTJfq" }, "source": [ "### Schéma de Nylström à 2 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{n+1}=u_{n-1}+2h\\varphi(t_{n},u_{n})& n=1,2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 165, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "BCR9Z7VzTxEN" }, "outputs": [], "source": [ "def N2(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " k1 = phi( tt[i], uu[i] )\n", " uu.append( uu[i-1] + 2*h*k1 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "dADQEhyYTVQz" }, "source": [ "### Schéma de Nylström à 3 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=u_{n-1}+\\frac{h}{3}\\Bigl(7\\varphi(t_{n},u_{n})-2\\varphi(t_{n-1},u_{n-1})+\\varphi(t_{n-2},u_{n-2})\\Bigr)& n=2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 166, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "bS1FABgRTzdC" }, "outputs": [], "source": [ "def N3(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " for i in range(2,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " uu.append( uu[i-1] + (7*k1-2*k2+k3)*h/3 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "LsgdqQnfTf66" }, "source": [ "### Schéma de Nylström à 4 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{n+1}=u_{n-1}+\\frac{h}{3}\\Bigl(8\\varphi(t_{n},u_{n})-5\\varphi(t_{n-1},u_{n-1})+4\\varphi(t_{n-2},u_{n-2})-\\varphi(t_{n-3},u_{n-3})\\Bigr)& n=3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 167, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "dbDTaW5LUcss" }, "outputs": [], "source": [ "def N4(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " uu.append( uu[i-1] + (8*k1-5*k2+4*k3-k4)*h/3 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "_50Xo95mT9tC" }, "source": [ "### Schéma de Runge-Kutta RK4-1\n", "$$\\begin{cases}\n", "u_0=y(t_0)=y_0,\\\\\n", "\\tilde u_{n+1/2}=u_n+\\frac{h}{2} \\varphi(t_{n},u_{n}),\\\\\n", "\\check u_{n+1/2}=u_n+\\frac{h}{2} \\varphi(t_{n}+\\frac{h}{2},\\tilde u_{n+1/2}),\\\\\n", "\\hat u_{n+1}=u_n+h\\varphi(t_{n+1},\\check u_{n+1/2}),\\\\\n", "u_{n+1}=u_n+\\frac{h}{6}\\left(\\varphi(t_{n},u_{n})+2\\varphi(t_{n}+\\frac{h}{2},\\tilde u_{n+1/2} )+2\\varphi(t_{n}+\\frac{h}{2}, \\check u_{n+1/2})+\\varphi(t_{n+1},\\hat u_{n+1} \\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 168, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "rbRn1INwGY-8" }, "outputs": [], "source": [ "def RK4(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i]+h/2 , uu[i]+h*k1/2 )\n", " k3 = phi( tt[i]+h/2 , uu[i]+h*k2/2 )\n", " k4 = phi( tt[i+1] , uu[i]+h*k3 )\n", " uu.append( uu[i] + (k1+2*k2+2*k3+k4)*h/6 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "_50Xo95mT9tC" }, "source": [ "### Schéma de Runge-Kutta RK6_5 (Butcher à 6 étages d'ordre 5)\n", "$$\\begin{array}{c|cccccc} 0 & 0 & 0 & 0 & 0 &0&0 \\\\ \\frac{1}{4} & \\frac{1}{4} & 0&0&0&0&0\\\\ \\frac{1}{4} & \\frac{1}{8} &\\frac{1}{8}&0&0&0&0\\\\ \\frac{1}{2} & 0 &-\\frac{1}{2}&1&0&0&0\\\\ \\frac{3}{4} & \\frac{3}{16} &0&0&\\frac{9}{16}&0&0\\\\ 1 & \\frac{-3}{7} &\\frac{2}{7}&\\frac{12}{7}&\\frac{-12}{7}&\\frac{8}{7}&0\\\\ \\hline & \\frac{7}{90} & 0&\\frac{32}{90} & \\frac{12}{90} & \\frac{32}{90} & \\frac{7}{90} \\end{array}$$\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 169, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "rbRn1INwGY-8" }, "outputs": [], "source": [ "def RK6_5(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " k1 = phi( tt[i] , uu[i] )\n", " k2 = phi( tt[i]+h/4 , uu[i]+h*k1/4 )\n", " k3 = phi( tt[i]+h/4 , uu[i]+h*(k1+k2)/8 )\n", " k4 = phi( tt[i]+h/2 , uu[i]+h*(-k2+2*k3)/2 )\n", " k5 = phi( tt[i]+h*3/4, uu[i]+h*(3*k1+9*k4)/16 )\n", " k6 = phi( tt[i+1] , uu[i]+h*(-3*k1+2*k2+12*k3-12*k4+8*k5)/7 )\n", " uu.append( uu[i] + (7*k1+32*k3+12*k4+32*k5+7*k6)*h/90 )\n", " return uu\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "_50Xo95mT9tC" }, "source": [ "### Schéma de Runge-Kutta RK7_6 (Butcher à 7 étages d'ordre 6)\n", "$$\n", "\\begin{array}{c|ccccccc} \n", "0 & 0 & 0 & 0 & 0 &0&0&0 \\\\ \n", "\\frac{1}{2} & \\frac{1}{2} & 0&0&0&0&0&0\\\\ \n", "\\frac{2}{3} & \\frac{2}{9} &\\frac{4}{9}&0&0&0&0&0\\\\ \n", "\\frac{1}{3} & \\frac{7}{36} &\\frac{2}{9}&-\\frac{1}{12}&0&0&0&0\\\\ \n", "\\frac{5}{6} & -\\frac{35}{144} &-\\frac{55}{36}&\\frac{35}{48}&\\frac{15}{8}&0&0&0\\\\ \n", "\\frac{1}{6} & -\\frac{1}{360} &-\\frac{11}{36}&-\\frac{1}{8}&\\frac{1}{2}&\\frac{1}{10}&0&0\\\\ \n", "1 & \\frac{-41}{260} &\\frac{22}{13}&\\frac{43}{156}&-\\frac{118}{39}&\\frac{32}{195}&\\frac{80}{39}&0\\\\ \n", "\\hline \n", " & \\frac{13}{200} & 0&\\frac{11}{40} & \\frac{11}{40} & \\frac{4}{25} & \\frac{4}{25} & \\frac{13}{200} \\end{array}$$\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 170, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "rbRn1INwGY-8" }, "outputs": [], "source": [ "def RK7_6(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " k1 = phi( tt[i] , uu[i] )\n", " k2 = phi( tt[i]+h/2 , uu[i]+h*( k1 )/2 )\n", " k3 = phi( tt[i]+h*2/3, uu[i]+h*( 2*k1 +4*k2 )/9 )\n", " k4 = phi( tt[i]+h/3 , uu[i]+h*( 7*k1 +8*k2 -3*k3 )/36 )\n", " k5 = phi( tt[i]+h*5/6, uu[i]+h*( -35*k1 -220*k2 +105*k3 +270*k4 )/144 )\n", " k6 = phi( tt[i]+h/6 , uu[i]+h*( -k1 -110*k2 -45*k3 +180*k4 +36*k5 )/360 )\n", " k7 = phi( tt[i+1] , uu[i]+h*(-41/260*k1 +22/13*k2 +43/156*k3 -118/39*k4 +32/195*k5 +80/39*k6) )\n", " uu.append( uu[i] + (13/200*k1+11/40*k3+11/40*k4+4/25*k5+4/25*k6+13/200*k7)*h )\n", " return uu " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Schémas implicites" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "y69SGZjfIDo9" }, "source": [ "### Schéma d'Euler régressif\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi(t_{n+1},u_{n+1})& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "avec $u_{n+1}$ zéro de la fonction $$x\\mapsto -x+u_n+h\\varphi(t_{n+1},x).$$" ] }, { "cell_type": "code", "execution_count": 171, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "_Bgo6mNyIQgu" }, "outputs": [], "source": [ "def EI(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*phi(tt[i+1],x), uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de Crank-Nicolson\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},u_{n+1})\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "avec $u_{n+1}$ un zéro de la fonction $x\\mapsto -x+u_n+\\frac{h}{2}(\\varphi(t_n,u_n)+\\varphi(t_{n+1},x))$." ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [], "source": [ "def CN(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " temp = fsolve(lambda x: -x+uu[i]+0.5*h*( phi(tt[i+1],x)+phi(tt[i],uu[i]) ), uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-2\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{n+1}=u_n+\\frac{h}{12}\\Bigl(5\\varphi(t_{n+1},u_{n+1})+8\\varphi(t_n,u_n)-\\varphi(t_{n-1},u_{n-1})\\Bigr)& n=1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 173, "metadata": {}, "outputs": [], "source": [ "def AM2(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*( 5*phi(tt[i+1],x)+8*phi(tt[i],uu[i])-phi(tt[i-1],uu[i-1]) )/12, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-3\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=u_n+\\frac{h}{24}\\Bigl(9\\varphi(t_{n+1},u_{n+1})+19\\varphi(t_n,u_n)-5\\varphi(t_{n-1},u_{n-1})+\\varphi(t_{n-2},u_{n-2})\\Bigr)& n=2,3,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 174, "metadata": {}, "outputs": [], "source": [ "def AM3(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tfor i in range(2,N):\n", "\t\ttemp = fsolve(lambda x: -x+uu[i]+h*( 9*phi(tt[i+1],x)+19*phi(tt[i],uu[i])-5*phi(tt[i-1],uu[i-1])+phi(tt[i-2],uu[i-2]) )/24, uu[i])[0]\n", "\t\tuu.append(temp)\n", "\treturn uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-4\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{n+1}=u_n+\\frac{h}{720}\\Bigl(251\\varphi(t_{n+1},u_{n+1})+646\\varphi(t_n,u_n)-264\\varphi(t_{n-1},u_{n-1})+106\\varphi(t_{n-2},u_{n-2})-19\\varphi(t_{n-3},u_{n-3})\\Bigr)& n=3,4,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [], "source": [ "def AM4(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tuu.append(sol_exacte(tt[3]))\n", "\tfor i in range(3,N):\n", "\t\ttemp = fsolve(lambda x: -x+uu[i]+h*( 251*phi(tt[i+1],x)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720, uu[i])[0]\n", "\t\tuu.append(temp)\n", "\treturn uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-5\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{4}=y_4,\\\\\n", "u_{n+1}=u_n+\\frac{h}{1440}\\Bigl(475\\varphi(t_{n+1},u_{+1})+1427\\varphi(t_n,u_n)-798\\varphi(t_{n-1},u_{n-1})+482\\varphi(t_{n-2},u_{n-2})-173\\varphi(t_{n-3},u_{n-3})+27\\varphi(t_{n-4},u_{n-4})\\Bigr),& n=4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [], "source": [ "def AM5(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tuu.append(sol_exacte(tt[3]))\n", "\tuu.append(sol_exacte(tt[4]))\n", "\tfor i in range(4,N):\n", "\t\ttemp = fsolve(lambda x: -x+uu[i]+h*( 475*phi(tt[i+1],x)+1427*phi(tt[i],uu[i])-798*phi(tt[i-1],uu[i-1])+482*phi(tt[i-2],uu[i-2])-173*phi(tt[i-3],uu[i-3])+27*phi(tt[i-4],uu[i-4]))/1440, uu[i])[0]\n", "\t\tuu.append(temp)\n", "\treturn uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma MS-2\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{n+1}=u_{n-1}+\\frac{h}{3}\\Bigl(\\varphi(t_{n+1},u_{n+1})+4\\varphi(t_n,u_n)+\\varphi(t_{n-1},u_{n-1})\\Bigr)& n=1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [], "source": [ "def MS2(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " temp = fsolve(lambda x: -x+uu[i-1]+h*(phi(tt[i+1],x)+4*phi(tt[i],uu[i])+phi(tt[i-1],uu[i-1]) )/3, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma BDF2\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{n+1}=\\frac{4}{3}u_n-\\frac{1}{3}u_{n-1}+\\frac{2}{3}h\\varphi(t_{n+1},u_{n+1})& n=1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [], "source": [ "def BDF2(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tfor i in range(1,N):\n", "\t\ttemp = fsolve(lambda x: -x+4/3*uu[i]-1/3*uu[i-1] + 2/3*h*phi(tt[i+1],x) , uu[i])[0]\n", "\t\tuu.append(temp)\n", "\treturn uu " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma BDF3\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=\\frac{18}{11}u_n-\\frac{9}{11}u_{n-1}+\\frac{2}{11}u_{n-2}+\\frac{6}{11}h\\varphi(t_{n+1},u_{n+1})& n=2,3,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [], "source": [ "def BDF3(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tfor i in range(2,N):\n", "\t\ttemp = fsolve(lambda x: -x+18/11*uu[i]-9/11*uu[i-1] + 2/11*uu[i-2]+6/11*h*phi(tt[i+1],x) , uu[i])[0]\n", "\t\tuu.append(temp)\n", "\treturn uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Schémas predicteur-correcteur" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "p4f0txAsIwNG" }, "source": [ "### Schéma d'Euler modifié\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+\\frac{h}{2}\\varphi(t_n,u_n),\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(t_n+\\frac{h}{2},\\tilde u\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 180, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "O5rOYvtPI7TO" }, "outputs": [], "source": [ "def EM(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " k1 = h * phi( tt[i], uu[i] )\n", " uu.append( uu[i]+h*phi(tt[i]+h/2,uu[i]+k1/2) )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de Heun\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+h\\varphi(t_n,u_n)\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},\\tilde u)\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 181, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "1ewZyxhHRYxg" }, "outputs": [], "source": [ "def heun(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i+1], uu[i] + k1*h )\n", " uu.append( uu[i] + (k1+k2)*h/2 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma AM-4 AB-2/3/4/5\n", "\n" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [], "source": [ "def AM4AB2(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tuu.append(sol_exacte(tt[3]))\n", "\tfor i in range(3,N):\n", "\t\tk1 = phi( tt[i], uu[i] )\n", "\t\tk2 = phi( tt[i-1], uu[i-1] )\n", "\t\tpred = uu[i] + (3*k1-k2)*h/2\n", "\t\tuu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", "\treturn uu\n", "\t \n", "def AM4AB3(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tuu.append(sol_exacte(tt[3]))\n", "\tfor i in range(3,N):\n", "\t\tk1 = phi( tt[i], uu[i] )\n", "\t\tk2 = phi( tt[i-1], uu[i-1] )\n", "\t\tk3 = phi( tt[i-2], uu[i-2] )\n", "\t\tpred = uu[i] + (23*k1-16*k2+5*k3)*h/12\n", "\t\tuu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", "\treturn uu\n", "\t \n", "def AM4AB4(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tuu.append(sol_exacte(tt[3]))\n", "\tfor i in range(3,N):\n", "\t\tk1 = phi( tt[i], uu[i] )\n", "\t\tk2 = phi( tt[i-1], uu[i-1] )\n", "\t\tk3 = phi( tt[i-2], uu[i-2] )\n", "\t\tk4 = phi( tt[i-3], uu[i-3] )\n", "\t\tpred = uu[i] + (55*k1-59*k2+37*k3-9*k4)*h/24\n", "\t\tuu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", "\treturn uu\n", "\t \n", "def AM4AB5(phi,tt,y0):\n", "\th = tt[1]-tt[0]\n", "\tuu = [y0]\n", "\tuu.append(sol_exacte(tt[1]))\n", "\tuu.append(sol_exacte(tt[2]))\n", "\tuu.append(sol_exacte(tt[3]))\n", "\tuu.append(sol_exacte(tt[4])) \n", "\tfor i in range(4,N):\n", "\t\tk1 = phi( tt[i], uu[i] )\n", "\t\tk2 = phi( tt[i-1], uu[i-1] )\n", "\t\tk3 = phi( tt[i-2], uu[i-2] )\n", "\t\tk4 = phi( tt[i-3], uu[i-3] )\n", "\t\tk5 = phi( tt[i-4], uu[i-4] )\n", "\t\tpred = uu[i] + (1901*k1-2774*k2+2616*k3-1274*k4+251*k5)*h/720\n", "\t\tuu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", "\treturn uu\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "cnwNf75iGe0F" }, "source": [ "On initialise le problème de Cauchy" ] }, { "cell_type": "code", "execution_count": 183, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "OLLu4aFJFENg" }, "outputs": [], "source": [ "t0, y0, tfinal = 0, 1, 3" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ve4iOfOIGsYc" }, "source": [ "On définit la solution exacte:" ] }, { "cell_type": "code", "execution_count": 184, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "W3EcAN2eGz2j" }, "outputs": [], "source": [ "def sol_exacte(t):\n", "\treturn exp(t)\n", "\t#return exp(-t)\n", "\t#return sqrt(2.*t+1.)\n", "\t#return sqrt(t**2+1.)\n", "\t#return 1./sqrt(1.-2.*t)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "xpjn_ogYGo20" }, "source": [ "On définit l'équation différentielle : `phi` est une fonction python qui contient la fonction mathématique $\\varphi(t, y)$ dépendant des variables $t$ et $y$." ] }, { "cell_type": "code", "execution_count": 185, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "df9F-MXWGm2a" }, "outputs": [], "source": [ "def phi(t,y):\n", "\treturn y\n", "\t#return -y\n", "\t#return 1./y \n", "\t#return t/y \n", "\t#return y**3 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version de base\n", "\n", "Pour chaque schéma, on calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$, à savoir $N_k=2$, $2^2$, $2^3$, ... $2^{10}$). On sauvegarde les valeurs de $h_k$ dans le vecteur `H`. \n", "\n", "Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on sauvegarde toutes ces erreurs dans le vecteur `err_schema` de sort que `err_schema[k]` contient $e_k=\\max_{i=0,...,N_k}|y(t_i)-u_{i}|$ avec $N_k=2^{k+1}$." ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [], "source": [ "H = []\n", "\n", "err_ep = []\n", "err_AB2 = []\n", "err_AB3 = []\n", "err_AB4 = []\n", "err_AB5 = []\n", "err_N2 = []\n", "err_N3 = []\n", "err_N4 = []\n", "err_RK4 = []\n", "err_RK6_5 = []\n", "err_RK7_6 = []\n", "\n", "err_er = []\n", "err_CN = []\n", "err_AM2 = []\n", "err_AM3 = []\n", "err_AM4 = []\n", "err_AM5 = []\n", "err_BDF2 = []\n", "err_BDF3 = []\n", "err_MS2=[]\n", "\n", "err_em = []\n", "err_heun = []\n", "err_AM4AB2 = []\n", "err_AM4AB3 = []\n", "err_AM4AB4 = []\n", "err_AM4AB5 = []\n", "\n", "N=10\n", "for k in range(6):\n", "\tN += 50#2**(k+3)\n", "\th = (tfinal-t0)/N\n", "\tH.append(h)\n", "\ttt = [t0+i*h for i in range(N+1)]\n", "\tyy = [sol_exacte(t) for t in tt]\n", "\t# schemas explicites\n", "\tuu_ep = EE(phi,tt,y0)\n", "\tuu_AB2 = AB2(phi,tt,y0)\n", "\tuu_AB3 = AB3(phi,tt,y0)\n", "\tuu_AB4 = AB4(phi,tt,y0)\n", "\tuu_AB5 = AB5(phi,tt,y0)\n", "\tuu_N2 = N2(phi,tt,y0)\n", "\tuu_N3 = N3(phi,tt,y0)\n", "\tuu_N4 = N4(phi,tt,y0)\n", "\tuu_RK4 = RK4(phi,tt,y0)\n", "\tuu_RK6_5 = RK6_5(phi,tt,y0)\n", "\tuu_RK7_6 = RK7_6(phi,tt,y0)\n", "\t# schemas implicites\n", "\tuu_er = EI(phi,tt,y0)\n", "\tuu_CN = CN(phi,tt,y0)\n", "\tuu_AM2 = AM2(phi,tt,y0)\n", "\tuu_AM3 = AM3(phi,tt,y0)\n", "\tuu_AM4 = AM4(phi,tt,y0)\n", "\tuu_AM5 = AM5(phi,tt,y0)\n", "\tuu_BDF2 = BDF2(phi,tt,y0)\n", "\tuu_BDF3 = BDF3(phi,tt,y0)\n", "\tuu_MS2 = MS2(phi,tt,y0)\n", "\t# schemas predictor-corrector\n", "\tuu_em = EM(phi,tt,y0)\n", "\tuu_heun = heun(phi,tt,y0)\n", "\tuu_AM4AB2 = AM4AB2(phi,tt,y0)\n", "\tuu_AM4AB3 = AM4AB3(phi,tt,y0)\n", "\tuu_AM4AB4 = AM4AB4(phi,tt,y0)\n", "\tuu_AM4AB5 = AM4AB5(phi,tt,y0)\n", "\t# erreurs\n", "\terr_ep.append(max([abs(uu_ep[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AB2.append(max([abs(uu_AB2[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AB3.append(max([abs(uu_AB3[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AB4.append(max([abs(uu_AB4[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AB5.append(max([abs(uu_AB5[i]-yy[i]) for i in range(N+1)]))\n", "\terr_N2.append(max([abs(uu_N2[i]-yy[i]) for i in range(N+1)]))\n", "\terr_N3.append(max([abs(uu_N3[i]-yy[i]) for i in range(N+1)]))\n", "\terr_N4.append(max([abs(uu_N4[i]-yy[i]) for i in range(N+1)]))\n", "\terr_RK4.append(max([abs(uu_RK4[i]-yy[i]) for i in range(N+1)]))\n", "\terr_RK6_5.append(max([abs(uu_RK6_5[i]-yy[i]) for i in range(N+1)]))\n", "\terr_RK7_6.append(max([abs(uu_RK7_6[i]-yy[i]) for i in range(N+1)]))\n", "\t\n", "\terr_er.append(max([abs(uu_er[i]-yy[i]) for i in range(N+1)]))\n", "\terr_CN.append(max([abs(uu_CN[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM2.append(max([abs(uu_AM2[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM3.append(max([abs(uu_AM3[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM4.append(max([abs(uu_AM4[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM5.append(max([abs(uu_AM5[i]-yy[i]) for i in range(N+1)]))\n", "\terr_BDF2.append(max([abs(uu_BDF2[i]-yy[i]) for i in range(N+1)]))\n", "\terr_BDF3.append(max([abs(uu_BDF3[i]-yy[i]) for i in range(N+1)]))\n", "\terr_MS2.append(max([abs(uu_MS2[i]-yy[i]) for i in range(N+1)]))\n", "\t\n", "\terr_em.append(max([abs(uu_em[i]-yy[i]) for i in range(N+1)]))\n", "\terr_heun.append(max([abs(uu_heun[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM4AB2.append(max([abs(uu_AM4AB2[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM4AB3.append(max([abs(uu_AM4AB3[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM4AB4.append(max([abs(uu_AM4AB4[i]-yy[i]) for i in range(N+1)]))\n", "\terr_AM4AB5.append(max([abs(uu_AM4AB5[i]-yy[i]) for i in range(N+1)]))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "SnKKU27oGyQb" }, "source": [ "Pour estimer l'ordre de convergence on estime la pente de la droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$ en echelle logarithmique en utilisant la fonction `polyfit` basée sur la régression linéaire. \t" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "ySox-VsNGt8p" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EE\t 0.97\n", "AB2\t 1.98\n", "AB3\t 2.96\n", "AB4\t 3.94\n", "AB5\t 4.92\n", "N2\t 1.99\n", "N3\t 2.97\n", "N4\t 3.95\n", "RK4\t 3.98\n", "RK6_5\t 4.95\n", "RK7_6\t 6.18\n", "\n", "\n", "EI\t 1.04\n", "CN\t 2.00\n", "AM2\t 2.98\n", "AM3\t 3.96\n", "AM4\t 4.95\n", "AM5\t 5.93\n", "BDF2\t 1.97\n", "BDF3\t 2.95\n", "MS2\t 4.00\n", "\n", "\n", "EM\t 1.98\n", "Heun\t 1.98\n", "AM4AB2\t 2.95\n", "AM4AB3\t 3.94\n", "AM4AB4\t 4.93\n", "AM4AB5\t 4.76\n" ] } ], "source": [ "print ('EE\\t %1.2f' %(polyfit(log(H),log(err_ep), 1)[0]))\n", "print ('AB2\\t %1.2f' %(polyfit(log(H),log(err_AB2), 1)[0]))\n", "print ('AB3\\t %1.2f' %(polyfit(log(H),log(err_AB3), 1)[0]))\n", "print ('AB4\\t %1.2f' %(polyfit(log(H),log(err_AB4), 1)[0]))\n", "print ('AB5\\t %1.2f' %(polyfit(log(H),log(err_AB5), 1)[0]))\n", "print ('N2\\t %1.2f' %(polyfit(log(H),log(err_N2), 1)[0]))\n", "print ('N3\\t %1.2f' %(polyfit(log(H),log(err_N3), 1)[0]))\n", "print ('N4\\t %1.2f' %(polyfit(log(H),log(err_N4), 1)[0]))\n", "print ('RK4\\t %1.2f' %(polyfit(log(H),log(err_RK4), 1)[0]))\n", "print ('RK6_5\\t %1.2f' %(polyfit(log(H),log(err_RK6_5), 1)[0]))\n", "print ('RK7_6\\t %1.2f' %(polyfit(log(H),log(err_RK7_6), 1)[0]))\n", "print('\\n')\n", "print ('EI\\t %1.2f' %(polyfit(log(H),log(err_er), 1)[0]))\n", "print ('CN\\t %1.2f' %(polyfit(log(H),log(err_CN), 1)[0]))\n", "print ('AM2\\t %1.2f' %(polyfit(log(H),log(err_AM2), 1)[0]))\n", "print ('AM3\\t %1.2f' %(polyfit(log(H),log(err_AM3), 1)[0]))\n", "print ('AM4\\t %1.2f' %(polyfit(log(H),log(err_AM4), 1)[0]))\n", "print ('AM5\\t %1.2f' %(polyfit(log(H),log(err_AM5), 1)[0]))\n", "print ('BDF2\\t %1.2f' %(polyfit(log(H),log(err_BDF2), 1)[0]))\n", "print ('BDF3\\t %1.2f' %(polyfit(log(H),log(err_BDF3), 1)[0]))\n", "print ('MS2\\t %1.2f' %(polyfit(log(H),log(err_MS2), 1)[0]))\n", "print('\\n')\n", "print ('EM\\t %1.2f' %(polyfit(log(H),log(err_em), 1)[0]))\n", "print ('Heun\\t %1.2f' %(polyfit(log(H),log(err_heun), 1)[0]))\n", "print ('AM4AB2\\t %1.2f' %(polyfit(log(H),log(err_AM4AB2), 1)[0]))\n", "print ('AM4AB3\\t %1.2f' %(polyfit(log(H),log(err_AM4AB3), 1)[0]))\n", "print ('AM4AB4\\t %1.2f' %(polyfit(log(H),log(err_AM4AB4), 1)[0]))\n", "print ('AM4AB5\\t %1.2f' %(polyfit(log(H),log(err_AM4AB5), 1)[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour les schémas AM4-ABx, on remarque que l'ordre du schéma predictor corrector est égale à celui du predictor +1. Par conséquente, si le schéma corrector est d'ordre $p$ (ici $p=5$ pour le schéma AM4), pour ne pas perdre en ordre convergence il faut choisir un schéma predictor d'ordre $p-1$ (ici AB4).\n", "Est-ce outil de choisir un predictor d'ordre $p$?" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "4HPS2hE6G54k" }, "source": [ "Pour afficher l'ordre de convergence on utilise une échelle logarithmique : on représente $\\ln(h)$ sur l'axe des abscisses et $\\ln(\\text{err})$ sur l'axe des ordonnées. Le but de cette représentation est clair: si $\\text{err}=Ch^p$ alors $\\ln(\\text{err})=\\ln(C)+p\\ln(h)$. En échelle logarithmique, $p$ représente donc la pente de la ligne droite $\\ln(\\text{err})$." ] }, { "cell_type": "code", "execution_count": 121, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 }, "base_uri": "https://localhost:8080/", "height": 3818, "output_extras": [ { "item_id": 1 }, { "item_id": 2 }, { "item_id": 3 }, { "item_id": 4 }, { "item_id": 5 }, { "item_id": 6 }, { "item_id": 7 }, { "item_id": 8 }, { "item_id": 9 }, { "item_id": 10 }, { "item_id": 11 } ] }, "colab_type": "code", "executionInfo": { "elapsed": 2188, "status": "ok", "timestamp": 1520423878951, "user": { "displayName": "Gloria Faccanoni", "photoUrl": "//lh4.googleusercontent.com/-gY6sCpFtBJo/AAAAAAAAAAI/AAAAAAAABdo/a_W4-RMG5X0/s50-c-k-no/photo.jpg", "userId": "116371262733782746288" }, "user_tz": -60 }, "id": "oz1tVYNtG4-3", "outputId": "9b89f5ec-83c5-4797-e057-8d6c20560051" }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(20,7))\n", "\n", "subplot(1,3,1)\n", "loglog(H,err_ep, 'r-o',label='AB-1=EE')\n", "loglog(H,err_AB2, 'g-+',label='AB-2')\n", "loglog(H,err_AB3, 'c-D',label='AB-3')\n", "loglog(H,err_AB4, 'y-*',label='AB-4')\n", "loglog(H,err_AB5, 'r-.',label='AB-5')\n", "loglog(H,err_N2, 'y-*',label='N-2')\n", "loglog(H,err_N3, 'r-<',label='N-3')\n", "loglog(H,err_N4, 'b-+',label='N-4')\n", "loglog(H,err_RK4, 'g-o',label='RK41')\n", "loglog(H,err_RK6_5, 'b-*',label='RK6_5')\n", "loglog(H,err_RK7_6, 'r-D',label='RK7_6')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas explicites\")\n", "legend() \n", "grid(True)\n", "\n", "subplot(1,3,2)\n", "loglog(H,err_er, 'r-o',label='AM-0=EI')\n", "loglog(H,err_CN, 'b-v',label='AM-1=CN')\n", "loglog(H,err_AM2, 'm->',label='AM-2')\n", "loglog(H,err_AM3, 'c-D',label='AM-3')\n", "loglog(H,err_AM4, 'g-+',label='AM-4')\n", "loglog(H,err_AM5, 'b->',label='AM-5')\n", "loglog(H,err_BDF2, 'y-*',label='BDF-2')\n", "loglog(H,err_BDF3, 'r-<',label='BDF-3')\n", "loglog(H,err_MS2, 'm-o',label='MS-2')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas implicites\")\n", "legend() \n", "grid(True)\n", "\n", "subplot(1,3,3)\n", "loglog(H,err_em, 'c-o',label='EM')\n", "loglog(H,err_heun, 'y->',label='Heun')\n", "loglog(H,err_AM4AB2, 'r-<',label='AM4-AB2')\n", "loglog(H,err_AM4AB3, 'b-v',label='AM4-AB3')\n", "loglog(H,err_AM4AB4, 'm-*',label='AM4-AB4')\n", "loglog(H,err_AM4AB5, 'g-+',label='AM4-AB5')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas predicteur-correcteur\")\n", "legend() \n", "grid(True)\n", "\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version compacte\n", "\n", "De manière compacte en utilisant une liste des noms des schémas et des dictionnaires:" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EE\t 0.97\n", "AB2\t 1.98\n", "AB3\t 2.96\n", "AB4\t 3.94\n", "AB5\t 4.92\n", "N2\t 1.99\n", "N3\t 2.97\n", "N4\t 3.95\n", "RK4\t 3.98\n", "RK6_5\t 4.95\n", "RK7_6\t 6.18\n", "EI\t 1.04\n", "CN\t 2.00\n", "AM2\t 2.98\n", "AM3\t 3.96\n", "AM4\t 4.95\n", "AM5\t 5.93\n", "BDF2\t 1.97\n", "BDF3\t 2.95\n", "MS2\t 4.00\n", "EM\t 1.98\n", "heun\t 1.98\n", "AM4AB2\t 2.95\n", "AM4AB3\t 3.94\n", "AM4AB4\t 4.93\n", "AM4AB5\t 4.76\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "schemasEXPL = ['EE','AB2','AB3','AB4','AB5','N2','N3','N4','RK4', 'RK6_5', 'RK7_6']\n", "schemasIMPL = ['EI', 'CN', 'AM2', 'AM3', 'AM4', 'AM5', 'BDF2', 'BDF3', 'MS2']\n", "schemasPRCO = ['EM', 'heun', 'AM4AB2', 'AM4AB3', 'AM4AB4', 'AM4AB5']\n", "\n", "schemas = schemasEXPL+schemasIMPL+schemasPRCO\n", "\n", "H = []\n", "err= { schemas[s] : [] for s in range(len(schemas)) }\n", "\n", "N=10\n", "for k in range(6):\n", " N += 50#2**(k+3)\n", " h = (tfinal-t0)/N\n", " H.append(h)\n", " tt = [t0+i*h for i in range(N+1)]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu = { schemas[s] : eval(schemas[s])(phi,tt,y0) for s in range(len(schemas)) }\n", " for s in range(len(schemas)):\n", " err[schemas[s]].append(max([abs(uu[schemas[s]][i]-yy[i]) for i in range(N+1)]))\n", "\n", " \n", "for s in range(len(schemas)):\n", " print (f'{schemas[s]}\\t {polyfit(log(H),log(err[schemas[s]]), 1)[0]:1.2f}')\n", "\n", "\n", " \n", "figure(figsize=(20,5))\n", "markers=['^', 's', 'p', 'h', '8', 'D', '>', '<', '*','+','o']\n", "\n", "subplot(1,3,1)\n", "for s in range(len(schemasEXPL)):\n", " loglog(H,err[schemasEXPL[s]], label=f'{schemasEXPL[s]}',marker=markers[s])\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas explicites\")\n", "legend()\n", "grid(True)\n", "\n", "subplot(1,3,2)\n", "for s in range(len(schemasIMPL)):\n", " loglog(H,err[schemasIMPL[s]], label=f'{schemasIMPL[s]}',marker=markers[s])\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas implicites\")\n", "legend()\n", "grid(True)\n", "\n", "subplot(1,3,3)\n", "for s in range(len(schemasPRCO)):\n", " loglog(H,err[schemasPRCO[s]], label=f'{schemasPRCO[s]}',marker=markers[s])\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas predicteur-correcteur\")\n", "legend()\n", "grid(True);\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "default_view": {}, "name": "EdoExplicites.ipynb", "provenance": [], "version": "0.3.2", "views": {} }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": true, "user_envs_cfg": true }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }